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Multiphase flow in a roll press nip

Published online by Cambridge University Press:  16 July 2002

A. D. FITT ,
P. D. HOWELL ,
J. R. KING ,
C. P. PLEASE  and
D. W. SCHWENDEMAN
A. D. FITT
Affiliation:
Faculty of Mathematical Studies, University of Southampton, Southampton SO17 1BJ, UK
P. D. HOWELL
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK
J. R. KING
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK
C. P. PLEASE
Affiliation:
Faculty of Mathematical Studies, University of Southampton, Southampton SO17 1BJ, UK
D. W. SCHWENDEMAN
Affiliation:
Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
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Abstract

A three-phase ensemble-averaged model is developed for the flow of water and air through a deformable porous matrix. The model predicts a separation of the flow into saturated and unsaturated regions. The model is closed by proposing an experimentally-motivated heuristic elastic law which allows large-strain nonlinear behaviour to be treated in a relatively straightforward manner. The equations are applied to flow in the ‘nip’ area of a roll press machine whose function is to squeeze water out of wet paper as part of the manufacturing process. By exploiting the thin-layer limit suggested by the geometry of the nip, the problem is reduced to a nonlinear convection-diffusion equation with one free boundary. A numerical method is proposed for determining the flow and sample simulations are presented.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 13 , Issue 3 , June 2002 , pp. 225 - 259
Copyright
2002 Cambridge University Press

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